Oblique Triangle and the Law of Cosines: Solving for Change in Piston Rate

[courtrigrad]

Hello all

I was given a problem involving cranks and pistons. I do not understand the exact question, but it involved an oblique triangle where you had to apply the Law of cosines. Let's say you are given $$\theta = \frac{\pi}{4}, x=7, c = 11$$ where $$c$$ where c is the hypotenuse and $$\frac{dx}{dt} = 200$$. Find the rate of change of the piston.

So here it is:

$$c^2 = a^2 + b^2 - 2ab\cos C$$
$$a^2 = b^2 + c^2 - 2bc\cos A$$
$$b^2 = a^2 + c^2 - 2ac\cos B$$


Ok so how would I solve for the change of the piston? Would I just find the derivative of the first Law of Cosine expression and substitute in the values?

 

[dextercioby]

Okay,what's the connection betweent the 4 variables:a,b,c & x??

Daniel.

 

[HallsofIvy]

What is x and what in the world is "the change of the piston"? (How does a piston change?)

 

[courtrigrad]

sorry I meant to say the rate of change of the piston . $$x$$ is one of the sides of the triangle.

 

[dextercioby]

Still doesn't make too much sense... :grumpy: What about a,b,c ?What are they...??

HINT:Post the initial problem's text in original form... :grumpy:


Daniel.